If you feel that graphics are important, then obviously you must be a shallow gamer who only plays HD iterations of big budget shooter X.
If you say they don't matter then surely you're a casual gamer loser or retro gamer snob.
This false dichotomy seems to represent the default positions on where people fall when presented with the question: Do graphics matter? But what do graphics really matter? As a graphic artist, you'd think I'd consider them pretty important, and you'd be right. However, I feel that the wrong question is being asked here.
Of course graphics matter, and asking if they matter more than game play is little more than a distraction. A far better question in my opinion is: What purpose do graphics serve?
I feel the role of the graphic is to support the art style.
During the preliminary stages of designing a game, one of the jobs of the artists is to determine the aesthetic theme for the game. This would (hopefully) be worked out in sketches and refined before any in game art resources are even made. The job of the graphic is to create that aesthetic in the game, and how well it succeeds is how it should be judged.
If a game seeks to recreate the look of an ink and watercolor painting and succeeds, then it has good graphics. If seeks to create the feel of crayons in a coloring book and succeeds, then it has good graphics. If it seeks to recreate the look of a vintage NES game and succeeds, then it has good graphics. If it seeks to recreate reality and looks like this:
...and the goal was not to make somebody with the eyes of a dead fish. Then the graphics aren't so good (hit and miss I'd say).
All I ask of those who would critique the look of a game is that you not confuse technically advanced graphics with good graphics. A chromed turd may be technically impressive with its reflections and refractions and shininess, but it's still a turd. And on the flip side, do not condemn a game for lacking the bells and whistles and advanced lighting and shading if the art style it's representing does not call for any of that.
As an artist, it's really no surprise I'd put all the emphasis on the art and see the graphics merely as the tool used to express that art. It's not the quality of paint that makes the masterpiece, it's what you do with the brush.
Related Links:
Too Many Crayons
Design Resurrection: How Capcom Finally Proved That It’s Game and Not Graphics That Matters
Abominations of Technology: Pre-Rendered Graphics